As you have not provided a clue of what your models are, one can only guess. 
But if you mean using lots of fixed effects vs a random effect, the answer is 
that there is no such animal.  They are two different non-nested models, and 
should be chosen based on subject matter considerations. Standard practice is 
to compare AIC, BIC and other "information criteria" but there is no clear 
standard to determine how large a difference is meaningful.

You may wish to post this on R-SIG-MIXED-MODELS for other inputs.

Bert

Sent from my iPhone -- please excuse typos.

On Apr 30, 2012, at 3:21 AM, "klai...@libero.it" <klai...@libero.it> wrote:

> Goodmorning everybody,
> i'm an italian statistician and i'm using R for research.
> 
> Could someone tell me some indices to see the goodness of fit in multilevel 
> modelling?
> I'm using the lmer function, and I want to know if my model fit well my 
> data.  
> I actually want to justify the use of multilevel model instead the classical 
> one.
> 
> Hope someone can help me. 
> Thank you.
> 
> Greetings 
> Chiara
> 
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